(CNN) -- Chrissie Hynde is an intimidating presence. Maybe it's her unflinching gaze and unapologetic swagger. Maybe it's the fact that she's the iconic lead singer of the Pretenders and a member of the Rock and Roll Hall of Fame.

"Not many guys come up to me," she admits matter of factly.

But someone did approach her nearly two years ago at a party in London -- a little-known Welsh singer-songwriter named JP Jones. They hit it off, flew to Cuba on a whim, holed up in the Hotel Nacional and wrote a tell-all album about finding your soul mate, but realizing your future together is doomed. Hynde turns 59 soon. Jones is 32.

"I've found my perfect lover, but he's only half my age," she sings in the opening track. Later in the record, he counters with, "Step aside for my bride, no you won't run and hide -- my love."

"This album is like the baby we could never have," Jones says.

Listening to the two trade vocals over the course of 11 songs is akin to eavesdropping on an intimate conversation between a couple as they fall in love and then contemplate breaking up. In this project, Hynde unveils an appealing vulnerability -- the antithesis of the tough-chick pout she displayed in such Pretenders anthems as "Tattooed Love Boys" and "Brass in Pocket."

The first -- and maybe last -- CD from JP, Chrissie and the Fairground Boys is called "Fidelity!"

"We wandered around Cuba," Hynde says. "Everywhere we went, there were pictures of Fidel Castro. So one day I said, 'If we did have a kid, we'd have to call it Fidel.' And then we looked at each other and said, 'We wouldn't have a boy, would we? We'd have a girl.' And 'Fidelity!' was born."

CNN spoke with Hynde and Jones as they were mixing the album in Pacific Palisades, California:

CNN: So this guy comes up to you at a party. What were you thinking?

Chrissie Hynde: I'm not really a party person. He walked up and said, "Hi."

CNN: JP, weren't you a little intimidated?

JP Jones: Well, you know -- alcohol? I don't know. I just wanted to go meet her. And we chatted loads and had a laugh.

Hynde: I said, "Look, it's too noisy in here. If you want to talk sometime, call me." And left basically. I went off on tour [with the Pretenders] the next day.

Jones: I just sort of kept texting her and sending her songs.

Hynde: Then I sort of got seduced by the songs. ... We weren't thinking about making an album. I was just burned out from the tour. ... And I just fancied going to Cuba. And I was sitting with him having a coffee, and I was like, "Do you fancy going to Cuba?" And he was like, "Yeah, let's go!" It was just spontaneous.

Jones: So we went like a week later, and I took a guitar. And we wrote an album. To each other.

Hynde: Yeah, we were each other's muse. We sat in restaurants and stuff, writing, looking at each other, writing lyrics down. We didn't decide anything stylistically, or what it was going to be about. We were just pouring out our hearts.

CNN: JP, was it interesting to hear what she was thinking about you and vice versa? Or were you already feeling this?

Jones: The whole album is about two people who can't be together for certain circumstances. That's all on the record.

CNN: What can't you be together?

Hynde: I'm too old. I can't have a family, and I've done that. He hasn't done that. So that was basically what this album's about.

CNN: What about making this into a movie? It'd be a great movie.

Hynde: Uh, pass.

CNN: Who could play the parts?

Hynde: I don't even want to go there. You know, I don't like that sort of biopic thing. We're musicians. We're singers. Our story is in our songs.

CNN: Do you ever look at the old photographs? --

Hynde: We hope that they stop looking at those old photographs. This album is my way of not being a legend, or having a legacy, or being in this Hall of Sh*t, you know. Just being now.

CNN: How did you go about picking "If You Let Me" as the single?

Hynde: I love this song because it's a rocker, and I wanted JP's voice to be the first thing heard when we come out. I'm very mindful of that, so that people don't think that he's, you know --

CNN: Protégé of?

Hynde: (Shrugs) I mean, I do feel a bit like Joan Baez, introducing him into the world. But they have to know who he is and how awesome he is, and why I did this with him. For the first time in my -- I suppose you could say "career" -- that I felt that I had anything to prove, because I've always just done what I wanted to do, and if anyone liked it, fair enough. And if they don't, fair enough. But I really want to show everyone who he is and say, "This is what I'm talking about."

CNN: Chrissie, you've been a supporter of PETA [People for the Ethical Treatment of Animals]. Their tactics have raised some eyebrows.

Hynde: Well, it's a punk organization. We believe that it's better to go too far than not far enough. Sometimes we've backed down and made an apology if we've offended someone, but it's more important to us to highlight the suffering of these 64 billion animals that are slaughtered for food every year.

CNN: JP, do you eat meat?

Jones: No.

CNN: Did she change that?

Jones: For a year before I met Chrissie, I was thinking about it a lot. I was obviously brought up eating meat and stuff, and so it was always really natural. And meeting her -- yeah, it was the catalyst for me. I haven't eaten it since we met, and I never, ever will again. It's just completely wrong. It's murder. I didn't know who I was before I met her. I was unconscious.

CNN: How comfortable is it sitting here talking about yourselves and your relationship?

Hynde: The weird thing is this innuendo about it all the time. You know, are they or aren't they?

CNN: But you understand why people ask?

Jones: It's all in the album. You gotta listen to the music, and everything is laid out on the line.

Hynde: There's just boundaries. Like I understand why I would maybe ask someone for their autograph, but I wouldn't go and ask them while they're eating. So you know -- be cool.